leave out vs rule out

leave out

verb
  • To omit, to not include, to neglect to mention. 

  • Used other than figuratively or idiomatically: see leave, out. 

rule out

verb
  • To disallow. 

  • To reject an option from a list of possibilities. 

  • To make something impossible. 

  • To cross an item out by drawing a straight line through it, as with a ruler. 

  • To make unavailable. 

How often have the words leave out and rule out occurred in a corpus of books? (source: Google Ngram Viewer )